The value of p and q (p ≠ 0, q ≠ 0) for which p, q are the roots of the equation
Question:

The value of $p$ and $q(p \neq 0, q \neq 0)$ for which $p, q$ are the roots of the equation $x^{2}+p x+q=0$ are

(a) p = 1, q = −2

(b) p = −1, q = −2

(c) p = −1, q = 2

(d) p = 1, q = 2

Solution:

(a) p = 1, q = −2

It is given that, $p$ and $q(p \neq 0, q \neq 0)$ are the roots of the equation $x^{2}+p x+q=0$.

$\therefore$ Sum of roots $=p+q=-p$

$\Rightarrow 2 p+q=0 \quad \ldots(1)$

Product of roots $=p q=q$

$\Rightarrow q(p-1)=0$

$\Rightarrow p=1, q=0$ but $q \neq 0$

Now, substituting p = 1 in (1), we get,

$2+q=0$

$\Rightarrow q=-2$

Disclaimer: The solution given in the book is incorrect. The solution here is created according to the question given in the book.